Non-equilibrium Solutions of Dynamic Networks: A Hybrid System Approach

Scott Greenhalgh () and Monica-Gabriela Cojocaru ()
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Scott Greenhalgh: Queen’s University
Monica-Gabriela Cojocaru: Univerity of Guelph

A chapter in Operations Research, Engineering, and Cyber Security, 2017, pp 299-315 from Springer

Abstract: Abstract Many dynamic networks can be analyzed through the framework of equilibrium problems. While traditionally, the study of equilibrium problems is solely concerned with obtaining or approximating equilibrium solutions, the study of equilibrium problems not in equilibrium provides valuable information into dynamic network behavior. One approach to study such non-equilibrium solutions stems from a connection between equilibrium problems and a class of parametrized projected differential equations. However, there is a drawback of this approach: the requirement of observing distributions of demands and costs. To address this problem we develop a hybrid system framework to model non-equilibrium solutions of dynamic networks, which only requires point observations. We demonstrate stability properties of the hybrid system framework and illustrate the novelty of our approach with a dynamic traffic network example.

Keywords: Dynamic networks; Hybrid systems; Variational inequalities; Equilibrium problems (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-51500-7_13

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DOI: 10.1007/978-3-319-51500-7_13

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